mathsurgery - GCSE SP2

GCSE Scheme of Work Foundation skillsfor first teaching 2007-2009

Topic reference:

SP2

Topic title:

Collecting & Representing Data

		Learning Objective	Links to Resources
7a	C	Pupils specify hypotheses in formal language (it is not necessary, but it may be desirable to introduce the ideas of null and alternate hypothesis to the brightest Reflect on the reliability of predictions made using lines-of-best-fit dependent on the strength of correlation shown. Pupils understand from examples that correlation does not imply a causal link and that some links do not lead to a (linear) correlation Use their line-of-best-fit to make predictions from a scatter diagram
7b		Pupils begin to say what they expect to find before they collect data and begin to refer to this as a ‘hypothesis’ Draw a line-of-best-fit on a scatter diagram (by inspection). A good technique is to cover as many points as possible with a transparent (15cm) ruler; mark the midpoints of the ends of the ruler and use these as a guide for the line, adjusting to ensure equal numbers of points either side. Comment on correlation using positive, negative and no correlation, together with adjectives ‘strong’ and ‘weak.’ Design and produce scatter diagrams using ICT, changing scales, axes, titles and other aspects of the graph’s appearance in the options tools and adding (linear) lines of best fit and their equations in Excel Design and produce scatter diagrams on (2mm) graph paper, choosing their own axes, adapting scales and omitting sections of the axes using the ‘zig zag’ notation to maximize detail and/or allow comparison
7c		Describe and interpret scatter diagrams in non-technical language: this goes up as that goes down Produce scatter diagrams using ICT, accepting the auto-scales given by Excel. Pupils complete and then produce simple scatter graphs on paper using pre-formatted axes then suggested axes on 5mm squared paper. Points should plot each pair of values as a small cross accurate to ½ a square respectively.
6a	D	Pupils use secondary data, from, for example, the internet, or printed lists and tables where the size of the data set is suitable to use unedited or quota sampling is condoned (i.e. “just look at the first 50 people”) Pupils construct frequency polygons on paper and using ICT, joining mid-points of class intervals of grouped data Pupils produce line graphs to show time-series such as temperature polygons (c.f. geography) or temperatures during cooling (c.f. science). These should be done on paper and using ICT. Pupils compare the presentation of data in bar charts and pie charts to decide which is better for comparing proportions, which for giving frequency values. Pupils construct and interpret pie charts where the total frequency is not a factor of 360º
6b		Pupils construct on paper and interpret pie charts to show quarters or eighths at first, then other suitable small factors of 360º onto pre-formatted circles, then using compasses and protractors. Pupils use ICT (Excel?) to produce and format pie charts to show categorical data
6c		Pupils use data logging equipment or simulations thereof (ask the science department to borrow equipment well in advance of the lesson?) Pupils conduct a controlled experiment to gather data (you might try the reaction times by dropping rulers through someone’s fingers: what are the controlled conditions here? How far apart should finger and thumb be before drop? Left or right handed?) Pupils collect and record continuous data into tables they have designed for themselves with appropriate equal class intervals Pupils collect and record continuous data (hand span or arm span?) into a pre-formatted table with equal class intervals. Pupils distinguish between continuous and discrete data, knowing that discrete data is always used for things that are counted and continuous data for things that are measured. The subtle possibility of discrete data taking non-integer values can be neatly shown by shoe sizes (note comparison with measuring the length of your feet). Another interesting issue is that for almost all people not still in primary education, age is discrete and time is continuous.
5a	E
5b
5c
4a	F
4b
4c
3a	G
3b
3c

GCSE Scheme of Work Higher skillsfor first teaching 2007-2009

Topic reference:

SP2

Topic title:

Collecting & Representing Data

		Learning Objective	Links to Resources
10a	A*
10b
10c
9a	A
9b		Pupils design and carry out ways of testing hypotheses using only appropriate methods (i.e. without redundant presentation or calculation) that anticipate variability and bias and seek to minimize it Pupils specify hypotheses in fully formal language (it is not necessary, but it may be desirable to introduce the ideas of null and alternate hypothesis to some pupils)
9c
8a	B	Pupils compare and interpret box and whisker diagrams to compare two distributions, describing location and spread Pupils create box and whisker diagrams from cumulative frequency curves Pupils use cumulative frequency curves to find values of a variate for the median, then lower and upper quartiles (LQ and UQ), finally finding values for any given percentile or quantile Pupils use cumulative frequency curves to find the frequency that satisfy a condition on the variate, e.g: “what percentage of cats weigh more than 5kg?”
8b		Pupils plot cumulative frequency diagrams on (A4) graph paper, designing their own axes to maximize the detail or make comparison easier, accurate to ½ a square. Pupils join points accurately with a single pencil line smooth curve (the typical shape is known as an ‘ogive,’ and should be anticipated but this term is not examinable) – again stress that the upper class boundaries are to be used as the x coordinates Pupils plot cumulative frequency diagrams on paper, plotting points on axes supplied on (2mm) graph paper accurate to 1 square and joining them with straight line segments to form a cumulative frequency polygon - it is essential that the upper class boundaries are used as the x coordinates
8c		Pupils complete, and later construct for themselves, cumulative frequency tables using “x ≤ 4” etc. as the class interval labels
7a	C	Pupils design and carry out ways of testing hypotheses using appropriate methods that begin to notice the effects of variability and bias Pupils specify hypotheses in more formal language Reflect on the reliability of predictions made using lines-of-best-fit dependent on the strength of correlation shown. Pupils understand from examples that correlation does not imply a causal link and that some links do not lead to a (linear) correlation Use their line-of-best-fit to make predictions from a scatter diagram
7b		Pupils begin to say what they expect to find before they collect data and begin to refer to this as a ‘hypothesis’ Draw a line-of-best-fit on a scatter diagram (by inspection). A good technique is to cover as many points as possible with a transparent (15cm) ruler; mark the midpoints of the ends of the ruler and use these as a guide for the line, adjusting to ensure equal numbers of points either side. Comment on correlation using positive, negative and no correlation, together with adjectives ‘strong’ and ‘weak.’ Design and produce scatter diagrams using ICT, changing scales, axes, titles and other aspects of the graph’s appearance in the options tools and adding (linear) lines of best fit and their equations in Excel Design and produce scatter diagrams on (2mm) graph paper, choosing their own axes, adapting scales and omitting sections of the axes using the ‘zig zag’ notation to maximize detail and/or allow comparison
7c		Describe and interpret scatter diagrams in non-technical language: this goes up as that goes down Produce scatter diagrams using ICT, accepting the auto-scales given by Excel. Pupils complete and then produce simple scatter graphs on paper using pre-formatted axes then suggested axes on 5mm squared paper. Points should plot each pair of values as a small cross accurate to ½ a square respectively.
6a	D	Pupils use secondary data, from, for example, the internet, or printed lists and tables where the size of the data set is suitable to use unedited or quota sampling is condoned (i.e. “just look at the first 50 people”) Pupils construct frequency polygons on paper and using ICT, joining mid-points of class intervals of grouped data Pupils produce line graphs to show time-series such as temperature polygons (c.f. geography) or temperatures during cooling (c.f. science). These should be done on paper and using ICT. Pupils compare the presentation of data in bar charts and pie charts to decide which is better for comparing proportions, which for giving frequency values. Pupils construct and interpret pie charts where the total frequency is not a factor of 360º
6b		Pupils construct on paper and interpret pie charts to show quarters or eighths at first, then other suitable small factors of 360º onto pre-formatted circles, then using compasses and protractors. Pupils use ICT (Excel?) to produce and format pie charts to show categorical data
6c		Pupils use data logging equipment or simulations thereof (ask the science department to borrow equipment well in advance of the lesson?) Pupils conduct a controlled experiment to gather data (you might try the reaction times by dropping rulers through someone’s fingers: what are the controlled conditions here? How far apart should finger and thumb be before drop? Left or right handed?) Pupils collect and record continuous data into tables they have designed for themselves with appropriate equal class intervals Pupils collect and record continuous data (hand span or arm span?) into a pre-formatted table with equal class intervals. Pupils distinguish between continuous and discrete data, knowing that discrete data is always used for things that are counted and continuous data for things that are measured. The subtle possibility of discrete data taking non-integer values can be neatly shown by shoe sizes (note comparison with measuring the length of your feet). Another interesting issue is that for almost all people not still in primary education, age is discrete and time is continuous.

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GCSE SP2